XI Phy Ch4 MotionInaPlane ChNotes Oct

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Class XI: PhysicsChapter 3: Motion in Plane

Chapter Notes

Key Learnings

1. Scalar quantities are quantities with magnitudes only. Examples are

distance, speed, mass and temperature.

2. Vector quantities are quantities with magnitude and direction both.

Examples are displacement, velocity and acceleration. They obey

special rules of vector algebra.

3. A vector A multiplied by a real number is also a vector, whose

magnitude dependent upon whether is positive or negative.

4. Two vectors A and B may be added graphically using head to tail

method or parallelogram method.

5. Vector addition is commutative:

A + B B + A

It also obeys the associative law:

(A + B) + C = A + (B+C)

6. A null or zero vector is a vector with zero magnitude. Since the

magnitude is zero, we dont have to specify its direction. It has sthe

properties:

A + O = A

O = O

OA = O

7. The subtraction of vector B from A is defined as the sum of A and B:

A B = A + (-B)


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8. A vector A can be resolved into component along two given vectors a

and b lying in the same plane:

A = a + b

Where and are real numbers.

9. A unit vector associated with a vector A has magnitude one and is

along the vector A:

An

A

The unit vectors

i, j,k are vectors of unit magnitude and point in the

direction of the x - , y - , and z axes, respectively in a right handed

coordinate system.

11. Two vectors can be added geometrically by placing them head to tail. The

vector connecting the tail of the first to the head of the second is the vector

sum or resultant vector.

12. Vector R can be resolved into perpendicular components given as Rx andRy along x and y axis respectively.ycos and R sin x R R R

An efficient method for adding vectors is using method of components.

13. Unit vectors i, j, and k have magnitudes of unity and are directed in thepositive direction of the x, y and z axes.

14. The position vector of particle at that instant is a vector that goes fromthe origin of the coordinate system to that point P.

15. The displacement vector is equal to the final position vector minus theinitial position vector.

16. Average velocity vector is equal to change in position vector divided bythe corresponding time interval.

17. Instantaneous velocity or simply velocity of a particle is along thetangent to the particles path at each instant


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18. Average acceleration is a vector quantity in the same direction as thevelocity vector.

19. Projectile is an object on which the only force acting is gravity.

20. The projectile motion can be thought of as two separate simultaneouslyoccurring components of motion along the vertical and horizontal directions.

21. During a projectiles flight its horizontal acceleration is zero and verticalacceleration is 9.8m/s 2 ..

22. The trajectory of particle in projectile motion is parabolic.

23. When a body P moves relative to a body B and B moves relative to A,then velocity of P relative to A is velocity of P relative to B + velocity of Prelative to A.

/ / / P A P B B AV V V

24. / / A B B AV V

25. When an object follows a circular path at constant speed, the motion of

the object is called uniform circular motion. The magnitude of its acceleration

is a c = v 2 / R. The direction of a c is always towards the centre of the circle.

26. The angular speed w, is the rate of change of angular distance. It is

related to velocity v by v = wR. The acceleration is a c = w 2 R.

27. If T is the time period of revolution of the object in circular motion and v

is the frequency, we have w = 2 vR, a c = 4 2v 2R


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Top Formulae:

Projectile Motion

Thrown at an angle with horizontal

(a)2

1 xy x tan .g.

2 u cos

x x

U u cos i a 0

y x

U u sin j a g j

Orx

y x tan 1R

(b) Time to reach max, height y

y

uu sint

g a

(c) Time of flight y

y

2u2u sinTg a

(d) Horizontal range2

xu sin2

R u Tg

(e) Max. height22y

maxy

uu sin2H

2g 2a

(f) Horizontal velocity at any time

xv u cos

(g) Vertical component of velocity at any time

yv u sin gt

(h) Resultant velocity x y

v v i v j

2 2 2

v u cos j u sin gt j

v v u g t 2ugt sin

And yx

vtan

v

General Result

For max. range = 45

Rmax =2u

g


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And H max = maxR

, at 45 and initial velocity u4

= maxR

; at 90 and initial velocity u2

(i) Change in momentum

(ii) For completer motion = 2 m u sin (iii) at highest point = m u sin Projectile thrown parallel to the horizontal

(a) Equation2

21 x

y g2 u

u x = u v x = u

u y = 0 v y = gt (down ward)

= -gt (upward)(b) velocity at any time

2 2 2v u g t

y

x

vtan

v

(c) Displacement S = x + y = ut + gt

(d) Time of Flight2h

Tg

(e) Horizontal range R =2hug

Projectile thrown from an inclined plane

x 0

a gsin i

y 0

x 0

y 0

a gcos j

u ucos i

u usin j

(a) Time of flight y 0y 0

2u 2usinT

a gcos


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0 0

0

0

00

1R ucos T gsin .T

22usin cos

Rgcos

2usin cosR gcos

Important for R max = 04 2

and R max = 0

ug 1 sin

Circular Motion

(a) angle (in radius) acradius

Or Sr

rad. = 180

(b) Angular velocity ( )

1. Instantaneous = ddt

2. Average av =total angular displacement

total time taken t

If v linear velocity

angular acceleration

a linear acceleration

(c) v = r In vector form v r

(d)ddt

(e) a = r and a r

Newtons equation in circular motion

= 0 + t = 0 t+ a t

= 0 2 + 2

Centripetal Force

Fc =mv

m r r

= m v

a c = cv

in vector F m v r


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Total Acceleration

a T = 2 2t ca a a T Tangential acceleration

a c Centripetal acceleration

Motion In Horizontal CircleT cos = mg

T sin = mv / r vtanrg

T = mg4v

1rg

The time period of revolution

T =h cos

2 2g g

Banking of Tracks

tan = vrg

, on frictionless road, banked by

Maximum speed for skidding, on circular un-banked road

vmax = rg

XI Phy Ch4 MotionInaPlane ChNotes Oct

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